Question

A​ 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental probability of rolling a number greater than 10.
Results
Number rolled
1
2
3
4
5
6
7
8
9
10
11
12
Total
Frequency
19
13
16
15
22
15
15
24
16
11
16
18
200
Question content area bottom
Part 1
The experimental probability of rolling a number greater than 10 is
  
enter your response here.
​(Simplify your​ answer.)

Answer 1

To find the experimental probability of rolling a number greater than 10, we first need to calculate how many times numbers greater than 10 (which are 11 and 12) were rolled.

From the table, the frequencies for the numbers are as follows:
- Frequency for 11: 16
- Frequency for 12: 18

Now, we can sum these frequencies:
\[ \text{Total frequency for numbers greater than 10} = 16 + 18 = 34 \]

Next, the experimental probability \( P \) is calculated using the formula:
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case:
- Number of favorable outcomes = 34 (rolling a number greater than 10)
- Total number of outcomes = 200 (total rolls)

Now we can substitute these values into the formula:
\[
P = \frac{34}{200}
\]

To simplify \( \frac{34}{200} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[
P = \frac{34 \div 2}{200 \div 2} = \frac{17}{100}
\]

Thus, the experimental probability of rolling a number greater than 10 is:
\[
\frac{17}{100}
\]